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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On compositions of the loop and suspension functors
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by M. H. Eggar PDF
Proc. Amer. Math. Soc. 123 (1995), 597-606 Request permission


The problem studied is whether, from knowledge of the homotopy type of ${\Omega ^{{d_k}}}{\Sigma ^{{c_k}}} \cdots {\Omega ^{{d_2}}}{\Sigma ^{{c_2}}}{\Omega ^{{d_1}}}{\Sigma ^{{c_1}}}X = MX$ for suitable spaces X, one can recover the nonnegative integers ${c_1},{d_1}, \ldots ,{c_k},{d_k}$. The Betti numbers of X and ${c_1},{d_1}, \ldots ,{c_k},{d_k}$ do determine the ith Betti number of MX, but even for small k , i and for X a sphere (say) the answer is a complicated one, since it depends on parities and graded Witt numbers depending on graded Witt numbers. It is shown that k can be found and that ${c_i},{d_j}$ can always be determined up to finitely many possibilities and usually uniquely.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 597-606
  • MSC: Primary 55P65; Secondary 55P62
  • DOI:
  • MathSciNet review: 1218114